The following result shows that Theorem REF  extends [1]}.
We start with some preliminaries.
A special class of Banach function spaces is the class of symmetric spaces (or rearrangement invariant Banach function spaces); see [2]}.
For a locally integrable weight \(w\)  on \(\mathbb {R}\) , we define \(\Vert \cdot \Vert _{\mathbb {E}_w}:L^0_+ \rightarrow [0,\infty ]\)  by \(\Vert f\Vert _{\mathbb {E}_w}: = \Vert  f^*_w\Vert _{\mathbb {E}}\) , where \(f^*_w\)  denotes the decreasing rearrangement of \(f\)  with respect to \(w \mathrm {d}t\) . By [2]}, the space
\(\mathbb {E}_w:= \lbrace  f\in L^0: \Vert f\Vert _{\mathbb {E}_w} <\infty \rbrace \) 
